The invention is based on a fuel injection pump as defined hereinafter. A fuel injection pump of this type is known from German Patent 37 66 313. In it, the onset and end of supply are controlled by an annular slide that is axially displaceable on the pump piston; the end edge of the annular slide controls the supply onset when the pump piston control recess enters the inner bore of the annular slide, and a radial control bore disposed in the peripheral wall of the annular slide, along with the control edge toward the pump work chamber of the oblique groove, controls the end of supply. Especially in fuel injection pumps that operate with a high injection pressure, problems in the diversion process occur. The high fuel pressures of up to 1300 bar that arise during the supply stroke have to be dissipated as rapidly as possible, in order by means of a steep pressure drop in the injection line to attain the fastest possible injection valve needle closure, and thus to reduce particle emissions.